def nuts(data, model, seed=None, iter=None, warmup=None, num_chains=None):
assert type(data) == dict
assert type(model) == Model
assert seed is None or type(seed) == int
iter, warmup, num_chains = apply_default_hmc_args(iter, warmup, num_chains)
if seed is None:
seed = np.random.randint(0, 2**32, dtype=np.uint32).astype(np.int32)
rng = random.PRNGKey(seed)
kernel = NUTS(model.fn)
# TODO: We could use a way of avoid requiring users to set
# `--xla_force_host_platform_device_count` manually when
# `num_chains` > 1 to achieve parallel chains.
mcmc = MCMC(kernel, warmup, iter, num_chains=num_chains)
mcmc.run(rng, **data)
samples = mcmc.get_samples()
# Here we re-run the model on the samples in order to collect
# transformed parameters. (e.g. `b`, `mu`, etc.) Theses are made
# available via the return value of the model.
transformed_samples = run_model_on_samples_and_data(
model.fn, samples, data)
all_samples = dict(samples, **transformed_samples)
loc = partial(location, data, samples, transformed_samples, model.fn)
return Samples(all_samples, partial(get_param, all_samples), loc)
def test_binomial_stable(with_logits):
# Ref: https://github.com/pyro-ppl/pyro/issues/1706
warmup_steps, num_samples = 200, 200
def model(data):
p = numpyro.sample('p', dist.Beta(1., 1.))
if with_logits:
logits = logit(p)
numpyro.sample('obs',
dist.Binomial(data['n'], logits=logits),
obs=data['x'])
else:
numpyro.sample('obs',
dist.Binomial(data['n'], probs=p),
obs=data['x'])
data = {'n': 5000000, 'x': 3849}
kernel = NUTS(model=model)
mcmc = MCMC(kernel, warmup_steps, num_samples)
mcmc.run(random.PRNGKey(2), data)
samples = mcmc.get_samples()
assert_allclose(np.mean(samples['p'], 0), data['x'] / data['n'], rtol=0.05)
if 'JAX_ENABLE_x64' in os.environ:
assert samples['p'].dtype == np.float64
def run_inference(model, args, rng):
kernel = NUTS(model)
mcmc = MCMC(kernel,
args.num_warmup,
args.num_samples,
num_chains=args.num_chains)
mcmc.run(rng)
return mcmc.get_samples()
def run_inference(model, args, rng, X, Y, D_H):
if args.num_chains > 1:
rng = random.split(rng, args.num_chains)
start = time.time()
kernel = NUTS(model)
mcmc = MCMC(kernel, args.num_warmup, args.num_samples, num_chains=args.num_chains)
mcmc.run(rng, X, Y, D_H)
print('\nMCMC elapsed time:', time.time() - start)
return mcmc.get_samples()
def run_inference(model, args, rng, X, Y):
start = time.time()
kernel = NUTS(model)
mcmc = MCMC(kernel,
args.num_warmup,
args.num_samples,
num_chains=args.num_chains)
mcmc.run(rng, X, Y)
print('\nMCMC elapsed time:', time.time() - start)
return mcmc.get_samples()
def get_samples(rng, data, step_size, trajectory_length,
target_accept_prob):
kernel = kernel_cls(model,
step_size=step_size,
trajectory_length=trajectory_length,
target_accept_prob=target_accept_prob)
mcmc = MCMC(kernel,
warmup_steps,
num_samples,
num_chains=2,
chain_method=chain_method)
mcmc.run(rng, data)
return mcmc.get_samples()
def test_improper_normal():
true_coef = 0.9
def model(data):
alpha = numpyro.sample('alpha', dist.Uniform(0, 1))
loc = numpyro.param('loc',
0.,
constraint=constraints.interval(0., alpha))
numpyro.sample('obs', dist.Normal(loc, 0.1), obs=data)
data = true_coef + random.normal(random.PRNGKey(0), (1000, ))
kernel = NUTS(model=model)
mcmc = MCMC(kernel, num_warmup=1000, num_samples=1000)
mcmc.run(random.PRNGKey(0), data)
samples = mcmc.get_samples()
assert_allclose(np.mean(samples['loc'], 0), true_coef, atol=0.05)
def test_improper_prior():
true_mean, true_std = 1., 2.
num_warmup, num_samples = 1000, 8000
def model(data):
mean = numpyro.param('mean', 0.)
std = numpyro.param('std', 1., constraint=constraints.positive)
return numpyro.sample('obs', dist.Normal(mean, std), obs=data)
data = dist.Normal(true_mean, true_std).sample(random.PRNGKey(1), (2000, ))
kernel = NUTS(model=model)
mcmc = MCMC(kernel, num_warmup, num_samples)
mcmc.run(random.PRNGKey(2), data)
samples = mcmc.get_samples()
assert_allclose(np.mean(samples['mean']), true_mean, rtol=0.05)
assert_allclose(np.mean(samples['std']), true_std, rtol=0.05)
def test_predictive():
model, data, true_probs = beta_bernoulli()
mcmc = MCMC(NUTS(model), num_warmup=100, num_samples=100)
mcmc.run(random.PRNGKey(0), data)
samples = mcmc.get_samples()
predictive_samples = predictive(random.PRNGKey(1), model, samples)
assert predictive_samples.keys() == {"obs"}
predictive_samples = predictive(random.PRNGKey(1), model, samples,
return_sites=["beta", "obs"])
# check shapes
assert predictive_samples["beta"].shape == (100, 5)
assert predictive_samples["obs"].shape == (100, 1000, 5)
# check sample mean
assert_allclose(predictive_samples["obs"].reshape([-1, 5]).mean(0), true_probs, rtol=0.1)
def test_dirichlet_categorical(kernel_cls, dense_mass):
warmup_steps, num_samples = 100, 20000
def model(data):
concentration = np.array([1.0, 1.0, 1.0])
p_latent = numpyro.sample('p_latent', dist.Dirichlet(concentration))
numpyro.sample('obs', dist.Categorical(p_latent), obs=data)
return p_latent
true_probs = np.array([0.1, 0.6, 0.3])
data = dist.Categorical(true_probs).sample(random.PRNGKey(1), (2000, ))
kernel = kernel_cls(model, trajectory_length=1., dense_mass=dense_mass)
mcmc = MCMC(kernel, warmup_steps, num_samples, progress_bar=False)
mcmc.run(random.PRNGKey(2), data)
samples = mcmc.get_samples()
assert_allclose(np.mean(samples['p_latent'], 0), true_probs, atol=0.02)
if 'JAX_ENABLE_x64' in os.environ:
assert samples['p_latent'].dtype == np.float64
def test_uniform_normal():
true_coef = 0.9
num_warmup, num_samples = 1000, 1000
def model(data):
alpha = numpyro.sample('alpha', dist.Uniform(0, 1))
loc = numpyro.sample('loc', dist.Uniform(0, alpha))
numpyro.sample('obs', dist.Normal(loc, 0.1), obs=data)
data = true_coef + random.normal(random.PRNGKey(0), (1000, ))
kernel = NUTS(model=model)
mcmc = MCMC(kernel, num_warmup=num_warmup, num_samples=num_samples)
mcmc.run(random.PRNGKey(2),
data,
collect_warmup=True,
collect_fields=('z', 'num_steps', 'adapt_state.step_size'))
samples = mcmc.get_samples()
assert len(samples[0]['loc']) == num_warmup + num_samples
assert_allclose(np.mean(samples[0]['loc'], 0), true_coef, atol=0.05)
def test_prior_with_sample_shape():
data = {
"J": 8,
"y": np.array([28.0, 8.0, -3.0, 7.0, -1.0, 1.0, 18.0, 12.0]),
"sigma": np.array([15.0, 10.0, 16.0, 11.0, 9.0, 11.0, 10.0, 18.0]),
}
def schools_model():
mu = numpyro.sample('mu', dist.Normal(0, 5))
tau = numpyro.sample('tau', dist.HalfCauchy(5))
theta = numpyro.sample('theta',
dist.Normal(mu, tau),
sample_shape=(data['J'], ))
numpyro.sample('obs', dist.Normal(theta, data['sigma']), obs=data['y'])
num_samples = 500
mcmc = MCMC(NUTS(schools_model), num_warmup=500, num_samples=num_samples)
mcmc.run(random.PRNGKey(0))
assert mcmc.get_samples()['theta'].shape == (num_samples, data['J'])
def test_unnormalized_normal(kernel_cls, dense_mass):
true_mean, true_std = 1., 2.
warmup_steps, num_samples = 1000, 8000
def potential_fn(z):
return 0.5 * np.sum(((z - true_mean) / true_std)**2)
init_params = np.array(0.)
kernel = kernel_cls(potential_fn=potential_fn,
trajectory_length=9,
dense_mass=dense_mass)
mcmc = MCMC(kernel, warmup_steps, num_samples)
mcmc.run(random.PRNGKey(0), init_params=init_params)
hmc_states = mcmc.get_samples()
assert_allclose(np.mean(hmc_states), true_mean, rtol=0.05)
assert_allclose(np.std(hmc_states), true_std, rtol=0.05)
if 'JAX_ENABLE_x64' in os.environ:
assert hmc_states.dtype == np.float64
def test_logistic_regression(kernel_cls):
N, dim = 3000, 3
warmup_steps, num_samples = 1000, 8000
data = random.normal(random.PRNGKey(0), (N, dim))
true_coefs = np.arange(1., dim + 1.)
logits = np.sum(true_coefs * data, axis=-1)
labels = dist.Bernoulli(logits=logits).sample(random.PRNGKey(1))
def model(labels):
coefs = numpyro.sample('coefs', dist.Normal(np.zeros(dim),
np.ones(dim)))
logits = np.sum(coefs * data, axis=-1)
return numpyro.sample('obs', dist.Bernoulli(logits=logits), obs=labels)
kernel = kernel_cls(model=model, trajectory_length=10)
mcmc = MCMC(kernel, warmup_steps, num_samples)
mcmc.run(random.PRNGKey(2), labels)
samples = mcmc.get_samples()
assert_allclose(np.mean(samples['coefs'], 0), true_coefs, atol=0.21)
if 'JAX_ENABLE_x64' in os.environ:
assert samples['coefs'].dtype == np.float64
def test_correlated_mvn():
# This requires dense mass matrix estimation.
D = 5
warmup_steps, num_samples = 5000, 8000
true_mean = 0.
a = np.tril(0.5 * np.fliplr(np.eye(D)) +
0.1 * np.exp(random.normal(random.PRNGKey(0), shape=(D, D))))
true_cov = np.dot(a, a.T)
true_prec = np.linalg.inv(true_cov)
def potential_fn(z):
return 0.5 * np.dot(z.T, np.dot(true_prec, z))
init_params = np.zeros(D)
kernel = NUTS(potential_fn=potential_fn, dense_mass=True)
mcmc = MCMC(kernel, warmup_steps, num_samples)
mcmc.run(random.PRNGKey(0), init_params=init_params)
samples = mcmc.get_samples()
assert_allclose(np.mean(samples), true_mean, atol=0.02)
assert onp.sum(onp.abs(onp.cov(samples.T) - true_cov)) / D**2 < 0.02
def test_diverging(kernel_cls, adapt_step_size):
data = random.normal(random.PRNGKey(0), (1000, ))
def model(data):
loc = numpyro.sample('loc', dist.Normal(0., 1.))
numpyro.sample('obs', dist.Normal(loc, 1), obs=data)
kernel = kernel_cls(model,
step_size=10.,
adapt_step_size=adapt_step_size,
adapt_mass_matrix=False)
num_warmup = num_samples = 1000
mcmc = MCMC(kernel, num_warmup, num_samples)
mcmc.run(random.PRNGKey(1),
data,
collect_fields=('z', 'diverging'),
collect_warmup=True)
num_divergences = mcmc.get_samples()[1].sum()
if adapt_step_size:
assert num_divergences <= num_warmup
else:
assert_allclose(num_divergences, num_warmup + num_samples)
def main(args):
jax_config.update('jax_platform_name', args.device)
print('Simulating data...')
(transition_prior, emission_prior, transition_prob, emission_prob,
supervised_categories, supervised_words,
unsupervised_words) = simulate_data(
random.PRNGKey(1),
num_categories=args.num_categories,
num_words=args.num_words,
num_supervised_data=args.num_supervised,
num_unsupervised_data=args.num_unsupervised,
)
print('Starting inference...')
rng = random.PRNGKey(2)
start = time.time()
kernel = NUTS(semi_supervised_hmm)
mcmc = MCMC(kernel, args.num_warmup, args.num_samples)
mcmc.run(rng, transition_prior, emission_prior, supervised_categories,
supervised_words, unsupervised_words)
samples = mcmc.get_samples()
print('\nMCMC elapsed time:', time.time() - start)
print_results(samples, transition_prob, emission_prob)
def test_beta_bernoulli(kernel_cls):
warmup_steps, num_samples = 500, 20000
def model(data):
alpha = np.array([1.1, 1.1])
beta = np.array([1.1, 1.1])
p_latent = numpyro.sample('p_latent', dist.Beta(alpha, beta))
numpyro.sample('obs', dist.Bernoulli(p_latent), obs=data)
return p_latent
true_probs = np.array([0.9, 0.1])
data = dist.Bernoulli(true_probs).sample(random.PRNGKey(1), (1000, 2))
kernel = kernel_cls(model=model, trajectory_length=1.)
mcmc = MCMC(kernel,
num_warmup=warmup_steps,
num_samples=num_samples,
progress_bar=False)
mcmc.run(random.PRNGKey(2), data)
samples = mcmc.get_samples()
assert_allclose(np.mean(samples['p_latent'], 0), true_probs, atol=0.05)
if 'JAX_ENABLE_x64' in os.environ:
assert samples['p_latent'].dtype == np.float64
def test_chain(use_init_params, chain_method):
N, dim = 3000, 3
num_chains = 2
num_warmup, num_samples = 5000, 5000
data = random.normal(random.PRNGKey(0), (N, dim))
true_coefs = np.arange(1., dim + 1.)
logits = np.sum(true_coefs * data, axis=-1)
labels = dist.Bernoulli(logits=logits).sample(random.PRNGKey(1))
def model(labels):
coefs = numpyro.sample('coefs', dist.Normal(np.zeros(dim),
np.ones(dim)))
logits = np.sum(coefs * data, axis=-1)
return numpyro.sample('obs', dist.Bernoulli(logits=logits), obs=labels)
kernel = NUTS(model=model)
mcmc = MCMC(kernel, num_warmup, num_samples, num_chains=num_chains)
mcmc.chain_method = chain_method
init_params = None if not use_init_params else \
{'coefs': np.tile(np.ones(dim), num_chains).reshape(num_chains, dim)}
mcmc.run(random.PRNGKey(2), labels, init_params=init_params)
samples = mcmc.get_samples()
assert samples['coefs'].shape[0] == num_chains * num_samples
assert_allclose(np.mean(samples['coefs'], 0), true_coefs, atol=0.21)
def test_change_point():
# Ref: https://forum.pyro.ai/t/i-dont-understand-why-nuts-code-is-not-working-bayesian-hackers-mail/696
warmup_steps, num_samples = 500, 3000
def model(data):
alpha = 1 / np.mean(data)
lambda1 = numpyro.sample('lambda1', dist.Exponential(alpha))
lambda2 = numpyro.sample('lambda2', dist.Exponential(alpha))
tau = numpyro.sample('tau', dist.Uniform(0, 1))
lambda12 = np.where(
np.arange(len(data)) < tau * len(data), lambda1, lambda2)
numpyro.sample('obs', dist.Poisson(lambda12), obs=data)
count_data = np.array([
13,
24,
8,
24,
7,
35,
14,
11,
15,
11,
22,
22,
11,
57,
11,
19,
29,
6,
19,
12,
22,
12,
18,
72,
32,
9,
7,
13,
19,
23,
27,
20,
6,
17,
13,
10,
14,
6,
16,
15,
7,
2,
15,
15,
19,
70,
49,
7,
53,
22,
21,
31,
19,
11,
18,
20,
12,
35,
17,
23,
17,
4,
2,
31,
30,
13,
27,
0,
39,
37,
5,
14,
13,
22,
])
kernel = NUTS(model=model)
mcmc = MCMC(kernel, warmup_steps, num_samples)
mcmc.run(random.PRNGKey(4), count_data)
samples = mcmc.get_samples()
tau_posterior = (samples['tau'] * len(count_data)).astype(np.int32)
tau_values, counts = onp.unique(tau_posterior, return_counts=True)
mode_ind = np.argmax(counts)
mode = tau_values[mode_ind]
assert mode == 44
if 'JAX_ENABLE_x64' in os.environ:
assert samples['lambda1'].dtype == np.float64
assert samples['lambda2'].dtype == np.float64
assert samples['tau'].dtype == np.float64
def run_inference(dept, male, applications, admit, rng, args):
kernel = NUTS(glmm)
mcmc = MCMC(kernel, args.num_warmup, args.num_samples, args.num_chains)
mcmc.run(rng, dept, male, applications, admit)
return mcmc.get_samples()
def main(args):
jax_config.update('jax_platform_name', args.device)
print("Start vanilla HMC...")
nuts_kernel = NUTS(potential_fn=dual_moon_pe)
mcmc = MCMC(nuts_kernel, args.num_warmup, args.num_samples)
mcmc.run(random.PRNGKey(11), init_params=np.array([2., 0.]))
vanilla_samples = mcmc.get_samples()
adam = optim.Adam(0.001)
rng_init, rng_train = random.split(random.PRNGKey(1), 2)
guide = AutoIAFNormal(dual_moon_model, hidden_dims=[args.num_hidden], skip_connections=True)
svi = SVI(dual_moon_model, guide, elbo, adam)
svi_state = svi.init(rng_init)
print("Start training guide...")
last_state, losses = lax.scan(lambda state, i: svi.update(state), svi_state, np.zeros(args.num_iters))
params = svi.get_params(last_state)
print("Finish training guide. Extract samples...")
guide_samples = guide.sample_posterior(random.PRNGKey(0), params,
sample_shape=(args.num_samples,))
transform = guide.get_transform(params)
unpack_fn = guide.unpack_latent
_, potential_fn, constrain_fn = initialize_model(random.PRNGKey(0), dual_moon_model)
transformed_potential_fn = make_transformed_pe(potential_fn, transform, unpack_fn)
transformed_constrain_fn = lambda x: constrain_fn(unpack_fn(transform(x))) # noqa: E731
init_params = np.zeros(guide.latent_size)
print("\nStart NeuTra HMC...")
# TODO: exlore why neutra samples are not good
# Issue: https://github.com/pyro-ppl/numpyro/issues/256
nuts_kernel = NUTS(potential_fn=transformed_potential_fn)
mcmc = MCMC(nuts_kernel, args.num_warmup, args.num_samples)
mcmc.run(random.PRNGKey(10), init_params=init_params)
zs = mcmc.get_samples()
print("Transform samples into unwarped space...")
samples = vmap(transformed_constrain_fn)(zs)
summary(tree_map(lambda x: x[None, ...], samples))
# make plots
# IAF guide samples (for plotting)
iaf_base_samples = dist.Normal(np.zeros(2), 1.).sample(random.PRNGKey(0), (1000,))
iaf_trans_samples = vmap(transformed_constrain_fn)(iaf_base_samples)['x']
x1 = np.linspace(-3, 3, 100)
x2 = np.linspace(-3, 3, 100)
X1, X2 = np.meshgrid(x1, x2)
P = np.clip(np.exp(-dual_moon_pe(np.stack([X1, X2], axis=-1))), a_min=0.)
fig = plt.figure(figsize=(12, 16), constrained_layout=True)
gs = GridSpec(3, 2, figure=fig)
ax1 = fig.add_subplot(gs[0, 0])
ax2 = fig.add_subplot(gs[0, 1])
ax3 = fig.add_subplot(gs[1, 0])
ax4 = fig.add_subplot(gs[1, 1])
ax5 = fig.add_subplot(gs[2, 0])
ax6 = fig.add_subplot(gs[2, 1])
ax1.plot(np.log(losses[1000:]))
ax1.set_title('Autoguide training log loss (after 1000 steps)')
ax2.contourf(X1, X2, P, cmap='OrRd')
sns.kdeplot(guide_samples['x'][:, 0].copy(), guide_samples['x'][:, 1].copy(), n_levels=30, ax=ax2)
ax2.set(xlim=[-3, 3], ylim=[-3, 3],
xlabel='x0', ylabel='x1', title='Posterior using AutoIAFNormal guide')
sns.scatterplot(iaf_base_samples[:, 0], iaf_base_samples[:, 1], ax=ax3, hue=iaf_trans_samples[:, 0] < 0.)
ax3.set(xlim=[-3, 3], ylim=[-3, 3],
xlabel='x0', ylabel='x1', title='AutoIAFNormal base samples (True=left moon; False=right moon)')
ax4.contourf(X1, X2, P, cmap='OrRd')
sns.kdeplot(vanilla_samples[:, 0].copy(), vanilla_samples[:, 1].copy(), n_levels=30, ax=ax4)
ax4.plot(vanilla_samples[-50:, 0], vanilla_samples[-50:, 1], 'bo-', alpha=0.5)
ax4.set(xlim=[-3, 3], ylim=[-3, 3],
xlabel='x0', ylabel='x1', title='Posterior using vanilla HMC sampler')
sns.scatterplot(zs[:, 0], zs[:, 1], ax=ax5, hue=samples['x'][:, 0] < 0.,
s=30, alpha=0.5, edgecolor="none")
ax5.set(xlim=[-5, 5], ylim=[-5, 5],
xlabel='x0', ylabel='x1', title='Samples from the warped posterior - p(z)')
ax6.contourf(X1, X2, P, cmap='OrRd')
sns.kdeplot(samples['x'][:, 0].copy(), samples['x'][:, 1].copy(), n_levels=30, ax=ax6)
ax6.plot(samples['x'][-50:, 0], samples['x'][-50:, 1], 'bo-', alpha=0.2)
ax6.set(xlim=[-3, 3], ylim=[-3, 3],
xlabel='x0', ylabel='x1', title='Posterior using NeuTra HMC sampler')
plt.savefig("neutra.pdf")
plt.close()
